On the Lagrangian Katz family of distributions as a claim frequency model

Gathy, Maude; Lefèvre, Claude

doi:10.1016/j.insmatheco.2010.03.010

Cited by 6 publications

(2 citation statements)

References 36 publications

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“…Since it is always possible to decompose into 0 and 0 translate directly into sequences of local alternatives to , which is equivalent to E[f( , θ)] = 0. Hall (1999) showed that for local alternatives given in (11) and (12), Jn(q) follows asymptotically a non-central χ 2 distribution. Furthermore, if the data satisfy .…”

Section: Local Power Analysismentioning

confidence: 99%

Specification Tests for Families of Discrete Distributions with Applications to Insurance Claims Data

Fang¹

2021

Journal of Data Science

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Families of distributions are commonly used to model insurance claims data that require flexible distributional forms in a satisfactory manner, but the specification problem to assess the goodness-of-fit of the hypothesized model can sometimes be a challenge due to the complexity of the likelihood function of the family of distributions involved. The previous work shows that these specification problems can be attacked by means of semi-parametric tests based on generalized method of moment (GMM) estimators. While the approach can be directly applied to both discrete and continuous families of distributions, the paper focuses on developing a testing strategy within a framework of discrete families of distributions. Both the local power analysis and the approximate slope method demonstrate the excellent performance of these tests. The finite-sample performance of the tests, based on both asymptotic and bootstrap critical values, are also discussed and are compared with established methods that require the complete specification of likelihood functions.

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Section: Local Power Analysismentioning

confidence: 99%

Specification Tests for Families of Discrete Distributions with Applications to Insurance Claims Data

Fang¹

2021

Journal of Data Science

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“…We present in Table 3 the fit for Tröbliger's data which has been published in 1961 (as cited by Gathy and Lefèvr [3]) on the frequency of the number of claims. This data set has an 87% proportion of zeros.…”

Section: Real Datamentioning

confidence: 99%

Generalized Sichel Distribution and Associated Inference

Low¹,

Ong²,

Gupta³

2017

JSTA

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In this paper, we propose a generalized form of Sichel distribution which is obtained by mixing the Poisson distribution with the extended generalized inverse Gaussian distribution. This distribution models over dispersed, zero-inflated and heavy-tailed count data sets. These characteristics are examined with respect to the dispersion, zero-inflation and the third central moment inflation indices. Examples are provided to compare the extension with several other existing models including the Poisson-inverse Gaussian and the Sichel distributions.

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Copula models for insurance claim numbers with excess zeros and time-dependence

Zhao

Zhou

2012

Insurance: Mathematics and Economics

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On the Lagrangian Katz family of distributions as a claim frequency model

Cited by 6 publications

References 36 publications

Specification Tests for Families of Discrete Distributions with Applications to Insurance Claims Data

Specification Tests for Families of Discrete Distributions with Applications to Insurance Claims Data

Generalized Sichel Distribution and Associated Inference

Copula models for insurance claim numbers with excess zeros and time-dependence

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